3. It's a 'Stabilized' or 'regulated' model.(Most modern types with replaceable tips and adjustable voltage is regulated.) A quick check is to measure the voltage output when it's not connected to anything. It should be within +/- .5V or so of 9V.

4. The plug must fit...

The most critical for you, since you have one that seems to fit is to check the amperage.My machine has a '4.5W' rating, which should suggest a max power draw of 500mA, but that's for 'normal running', and does not necessarily include the power used to recharge the battery.Using a PSU of less than 1000mA is 'not recommended', and if using one that's below 1500mA, I'd suggest plugging it in and letting it charge the battery fully before switching it on.